US5471101A

US5471101A - High efficiency electrical machine with minimized material content

Info

Publication number: US5471101A
Application number: US08/156,276
Authority: US
Inventors: Bruce T. Hein
Original assignee: MagneTek Century Electric Inc
Current assignee: AO Smith Corp
Priority date: 1993-11-22
Filing date: 1993-11-22
Publication date: 1995-11-28
Anticipated expiration: 2013-11-22

Abstract

An improved method is provided for the design of high-efficiency electric machines. The maximum practical value of air gap flux density Bg is selected, consistent with maintaining acceptable noise and vibration levels. The value of Bg selected is then used to determine the dimensions of the stator and rotor laminations so as to result in flux density levels that minimize core loss, stator I2R and rotor I2R losses, and magnetizing current requirements.

Description

BACKGROUND OF THE INVENTION

1. Technical Field

The present invention relates generally to the field of electric machines, e.g., motors and generators, and in particular to methods used to design high-efficiency electric machines.

2. Background Art

High efficiency has been a long-standing objective in the design and manufacture of electric machines. The prior art teaches that high efficiency is achieved by maximizing the amount of lamination material in the rotor and stator and then maximizing the amount of conductor wound onto the lamination material. Reactance is adjusted by increasing the number of series turns per coil in the winding.

The method used in the prior art necessarily results in greater costs. First, electric machines designed in this way necessarily require greater expenditures for lamination and winding material, as more is used. Further, using the maximum amount of winding material results in windings that are less adaptable to machine winding, thereby leading to increased labor costs.

The market for high-efficiency electric machines is competitive, and the savings of even a few cents per unit can be significant. There is thus a need in the art for a design method that minimizes material content.

SUMMARY OF INVENTION

The present invention provides an improved method for the design of high-efficiency electric machines. In a preferred embodiment of a method according to the present invention, the maximum practical value of air gap flux density B_g is selected, consistent with maintaining acceptable noise and vibration levels. The value of B_g selected is then used to determine the dimensions of the stator and rotor laminations so as to result in flux density levels that minimize core losses and magnetizing current requirements.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A shows a composite front view of a rotor and stator assembly, juxtaposing the upper half of a stator and rotor designed according to the prior art with the lower half of a stator and rotor designed according to a preferred embodiment of the present invention. FIG. 1B shows a cross section of the composite stator and rotor assembly taken through the plane 1-1.

FIG. 2 shows a block diagram of a method according to the prior art for designing high-efficiency electric machines.

FIG. 3 shows a block diagram of a preferred embodiment of a high air gap flux density design method according to the present invention for designing high-efficiency electric machines.

DESCRIPTION OF SPECIFIC EMBODIMENTS

FIG. 1A shows a composite front view of a stator and rotor assembly, juxtaposing the upper half of a stator and rotor designed according to the prior art and the lower half of a stator and rotor designed according to a preferred embodiment of a high air gap flux density design method according to the present invention. The particular stator and rotor shown are used in 10 HP 1800 RPM induction machines. FIG. 1B shows a cross section of the stator and rotor assembly taken through the plane 1-1.

As shown in FIGS. 1A and 1B, the

stator

10a, 10b comprises a hollow cylindrical body. The stator body is made up of a number of laminations, manufactured using materials and methods known in the art, and includes a set of

slots

12a, 12b, regularly spaced along its inner circumference, to receive coils of winding

material

14a, 14b, such as copper wire, or other conductor. The portion of the coils extending beyond either end of the stator body includes a straight section immediately proximate to the end of the stator body and a flared section extending from the distal end of the straight section to the nose of the coils.

As further shown in FIGS. 1A and 1B, the

rotor

16a, 16b comprises a cylindrical body fitting closely within the stator body, separated by an air gap. The rotor core is made up of a number of laminations, manufactured using materials and methods known in the art, and includes a set of

slots

18a, 18b along its outer circumference. The rotor includes end rings 20a, 20b extending beyond either end of the rotor body.

FIG. 2 shows a block diagram of a design method according to the prior art for maximizing the efficiency of an electric machine. The first step 22 is to determine the maximum amount of lamination material that will fit into the available physical envelope. The second step 24 is to use as large an amount of winding material as possible, without causing excessive core losses. Finally, in the third step 26, the reactance of the machine is adjusted by increasing the number of series turns per coil in the winding, in order to limit inrush currents to acceptance levels.

As is apparent from FIG. 2, the prior art method is premised on the assumption that the design of a highly efficient motor must begin with maximizing the amount of lamination and winding material used. Undesirable characteristics of the machine, such as reactance, are adjusted only after the amount of lamination and winding material used has been maximized.

The prior art approach thus necessarily leads to greater expenditures for materials. Further, maximizing the amount of winding material used and increasing the number of series turns per coil leads to windings that are less adaptable to machine winding, thereby resulting in increased labor costs.

The present invention provides a design method for high-efficiency electric machines that minimizes the amount of lamination and winding material used by maximizing the air gap flux density B_g. As is apparent from FIGS. 1A and 1B, use of the high air gap flux density design method results in an electric machine significantly smaller than a machine of comparable efficiency designed according to the prior art.

The present invention is based on the following relationships in electric machines, which generally apply to both motors and generators, with minor changes (for example, in a generator, kilowatts are used instead of horsepower):

(1) OUTPUT TORQUE ##EQU1## where T_MAX =Maximum output torque (basis of machine rating), usually expressed as a percentage of the full load torque

X=Total leakage reactance under running conditions, calculated in section (2), below

and where C₁ is a constant that is computed as follows: ##EQU2## where m=Number of phases in the winding (usually three)

E.sub.ψ =Voltage per phase

HP=Horsepower rating for motors

These relationships can be used to calculate the maximum output torque T_MAX of the induction machine shown in FIG. 1B, in which m=3, E.sub.ψ =265, HP=10, and, as shown below in section (2), X=2.871. These values yield C₁ =1002.8, and T_MAX =349%.

(2) LEAKAGE REACTANCE

X=C.sub.2 ·N.sup.2 (C.sub.3 L+C.sub.4)

where

N=Number of series turns per coil in the winding

L=Axial length of the laminations

C₂ is a constant, computed as follows: ##EQU3## where Q₁ =Number of stator slots

f=Frequency of the voltage supply

a=Number of parallel circuits used in the stator winding

C₃ is a constant, computed as follows: ##EQU4## where m=Number of phases in the winding, usually three

Q₁ =Number of stator slots

_T K_S =A geometric factor for the body section of the stator slot

_T K_X =A reactance chord factor for that part of the slot above the coil; this factor is related to the percentage pitch used in the winding

_A K_S =A geometric factor for the top section of the stator slot

_A K_X =A reactance chord factor for that part of the slot where the winding lies; this factor is related to the percentage pitch used in the winding

Q₂ =Number of rotor slots

K_C =A factor related to the chording or percentage pitch of the winding

K_D =A factor related to the distribution of the winding in terms of slots per pole

₂ K_S /(RUN)=A geometric factor for the body section of the rotor slot under running conditions

₁ D_i =Inside diameter of the stator

g_eq =Equivalent length of the air gap between the stator and rotor

P=Number of poles that the machine is wound for

Q_SK =Number of slots skewed as a fraction of a stator slot pitch

C₄ is a constant, computed as follows: ##EQU5## where C=Straight portion of winding coil extension

Z=Axial end coil distance from the end of the straight portion of the coil to the nose of the coil

₂ D_o =Outside diameter of the rotor

b_er =Depth of rotor end ring

h₁ =Depth of stator slot

a_er =Width of rotor end ring

The induction machine shown in FIG. 1B displays the following values for these parameters:

______________________________________                                    
N =         26          .sub.2 K.sub.S =                                  
                                1.914                                     
L =         3.75        (RUN)                                             
Q.sub.1 =   36          .sub.1 D.sub.i =                                  
                                4.770                                     
f =         60          g.sub.eq =                                        
                                .0183                                     
a =         2           p =     4                                         
m =         3           Q.sub.SK =                                        
                                1.2                                       
.sub.T K.sub.S =                                                          
            1.80        C =     .25                                       
.sub.T K.sub.X =                                                          
            .937        Z =     1.614                                     
.sub.A K.sub.S =                                                          
            .714        .sub.2 D.sub.o =                                  
                                4.740                                     
.sub.A K.sub.X =                                                          
            .915        b.sub.er =                                        
                                1.340                                     
Q.sub.2 =   44          h.sub.1 =                                         
                                .734                                      
K.sub.C =   .985        a.sub.er =                                        
                                .370                                      
K.sub.D =   .960                                                          
______________________________________

Using these values in the above equations yields the following results: C₂ =7.776×-10^-4, C₃ =1.169, C₄ =1.077, and X=2.871.

(3) RESISTANCE (PER PHASE) ##EQU6## where A_x =Cross sectional area of a single series turn in the winding

and where C₅ and C₆ are constants, determined as follows: ##EQU7##

Applying these equations to the induction machine shown in FIG. 1B, in which

______________________________________                                    
N =        26            m =     3                                        
L =        3.75          a =     2                                        
A.sub.x =  .001608       L.sub.EC =                                       
                                 5.93                                     
Q.sub.1 =  36                                                             
______________________________________

yields the following results: C₅ =4.152×10^-6, C₆ =5.93, and R=0.649

(4) AIR GAP FLUX DENSITY ##EQU8## where C₇ is a constant computed using the following formula: ##EQU9##

Using the values previously given as the parameters for the induction machine shown in FIG. 1B, C₇ is calculated to be 0.0679×10⁸, and B_g is calculated to be 69,640.

(5) WEIGHT OF WINDING MATERIAL ##EQU10## where WT=Winding weight

and where C₈ and C₆ are constants, calculated as follows:

C.sub.8 =0.650 Q.sub.1

C.sub.6 =L.sub.EC

Applying these equations to the values previously given for the parameters of the induction machine shown in FIG. 1B, C₆ is 5.93, C₈ is calculated to be 23.4, and WT is calculated to be 9.47.

The above relationships for output torque, leakage reactance, resistance, and weight of winding material can be restated as follows to show their relationship to air gap flux density (B_g):

(6) OUTPUT TORQUE ##EQU11## where C₉ is a constant, calculated as follows: ##EQU12##

Applying these relationships to the values previously given for the parameters of the induction machine shown in FIG. 1B, C₉ is calculated to be 35.75×10⁶, and T_MAX is calculated to be 349.9% (as compared with 349% obtained above using the relationships set forth in section (1).

Further, using the restated relationships, it can be shown that where a B_g of 40,000 is used instead of 69,700, then L is calculated to be 9.98, as compared with an L of 3.75 for a B_g of 69,640.

(7) LEAKAGE REACTANCE ##EQU13## where C₁₀ is a constant, determined by the following formula:

C.sub.10 =C.sub.2 ·C.sub.7.sup.2

Applying these relationships to the values previously given for the parameters of the induction machine shown in FIG. 1B, C₁₀ is calculated to be 3.585×10¹⁰, and X is calculated to be 2.866 (as compared with 2.871, arrived at using the relationships set forth above in section (2).

Using the restated relationships, it can be shown that where a B_g of 40,000 is used, L becomes 9.98.

(8) RESISTANCE (PER PHASE) ##EQU14## where C₁₁ is a constant, calculated as follows:

C.sub.11 =C.sub.5 ·C.sub.7

Applying these relationships to the values previously given for the parameters of the induction machine shown in FIG. 1B, C₁₁ is calculated to be 28.19, and R is calculated to be 0.649 (the same value arrived at using the relationships set forth above in section 15D).

Using the restated relationships, it can be shown that where a B_g of 40,000 is used, L becomes 7.78.

(9) WEIGHT OF WINDING MATERIAL ##EQU15## where C₁₂ is constant, calculated as follows:

C.sub.12 =C.sub.7 ·C.sub.8

Applying these relationships to the values previously given for the parameters of the induction machine shown in FIG. 1B, C₁₂ is calculated to be 1.589×10⁸, and WT is calculated to be 9.46 (as compared with 9.47, arrived at using the prior art relationships).

Using the restated relationships, where a B_g of 40,000 is used, L becomes 7.78, and WT becomes 13.40.

Thus, from the above equations, it follows that as the air gap magnetic flux B_g increases, the following desirable results can be obtained: First, T_MAX, the output torque, can be achieved with a lower value for L, the axial length of the laminations. Second, a specific value of X, the total leakage reactance under running conditions, can be achieved with a lower value for L. Third, a lower value of R, the resistance of the winding, can be obtained for a specific value of A_x, the cross sectional area of a single series turn in the winding. Finally, a lower value of WT, the winding weight, can be obtained for a specific value of A_x. It thus appears that it is possible to achieve equal or greater efficiency in an electric machine with less lamination and winding material, by maximizing the air gap magnetic flux B_g.

FIG. 3 shows a block diagram of a preferred embodiment of a method according to the present invention. In the first step 28, a maximum value of the air gap magnetic flux B_g is selected, consistent with maintaining acceptable noise and vibration levels. It is this maximum value for B_g that provides the basis for the design of the machine.

In the second step 30, the value of B_g selected is used to determine the other dimensions of the stator and rotor laminations so as to result in flux density levels that minimize core losses and magnetizing current requirements.

The determination of the other dimensions also requires evaluating I² R losses in both the stator and rotor windings, with adjustments being made until the summation of the core loss, stator I² R loss and rotor I² R loss is minimized. This is carried out in the third and fourth steps 32, 34.

The final step 36 is to shape the rotor slots so as to result in the amount of slot leakage reactance required to limit inrush currents to acceptable levels and/or levels mandated by industry standards.

Typically, electric machines designed using the high air gap flux density design method will have air gap flux densities in the range of 55-75 KL/in². Those designed using prior art methods will typically have air gap flux densities in the range of 35-50 KL/in².

While the foregoing description includes detail which will enable those skilled in the art to practice the invention, it should be recognized that the description is illustrative in nature and that many modifications and variations will be apparent to those skilled in the art having the benefit of these teachings. It is accordingly intended that the invention herein be defined solely by the claims appended hereto and that the claims be interpreted as broadly as permitted in light of the prior art.

Claims

I claim:

1. An electrical machine having minimized material content, comprising a laminated stator and rotor with the laminations designed by:

(a) selecting the maximum practical value of air gap flux density B_g consistent with maintaining acceptable noise and vibration levels;

(b) using the value of B_g selected to determine the dimensions of the stator and rotor laminations so as to result in flux density levels that minimize core losses and magnetizing current requirements.

2. An electrical machine according to claim 1, wherein the dimensions of the stator and rotor laminations are determined by applying the relationship: ##EQU16## where N is the number of series turns per coil in the winding, L is the axial length of the laminations, and C is a constant, computed using the following formula: ##EQU17## where p=the number of poles the machine is wound for;

E.sub.ψ =the voltage per phase;

m=the number of phases in the winding;

a=the number of parallel circuits used in the stator winding;

.sub. D_i =the inside diameter of the stator;

f=the frequency of the voltage supply;

Q₁ =the number of rotor slots;

K_c =a factor related to the chording of the winding; and

K_D =a factor related to the distribution of the winding in terms of slots per pole.

3. An electrical machine according to claim 2, wherein the dimensions of the stator and rotor laminations are further determined by evaluating I² R losses in both the stator and rotor windings and adjusting the dimensions of the stator and rotor laminations and the windings until the summation of the core loss, stator I² R loss and rotor I² R loss is minimized.

4. An electrical machine according to claim 3 wherein the rotor slots are shaped so as to result in the amount of slot leakage reactance required to limit inrush currents.

5. An electrical machine having minimized material content, comprising a laminated stator and rotor with the laminations designed by:

(a) selecting as an initial parameter the maximum practical value of air gap flux density consistent with maintaining acceptable noise and vibration levels;

(b) selecting dimensions for the stator and rotor laminations based upon the selected value of air gap flux density;

(c) evaluating I² R loss in the stator winding;

(d) evaluating I² R loss in the rotor winding;

(e) evaluating core loss in the stator and rotor laminations;

(f) adjusting the dimensions of the stator and rotor laminations and the stator and rotor windings until the summation of the core loss, stator I² R loss and rotor I² R loss is minimized; and

(g) shaping the rotor slots so as to result in the amount of slot leakage reactance required to limit inrush currents.